A class of matrices to test inversion procedures

Abstract

The test matrices given by M. L. Pei [ Comm. ACM 5 , 10 (Oct. 1962), 508] and R. D. Rodman [ Comm. ACM 6 , 9 (Sept. 1963, 515] are special cases of a general class of matrices with complex elements for which an explicit form of the inverse can be exhibited. This class of matrices is such that eigenvalues and a set of associated eigenvectors can also be obtained. Then not only inverses, but also eigenvalues of the Pei matrix given by W. S. Lasor [ Comm. ACM 6 , 3 (Mar. 1963), 102] and eigenvectors given by A. R. C. Newberry [ Comm. ACM 6 , 9 (Sept. 1963), 515], and eigenvalues of the Rodman matrix follow as special cases.